I think 13_gecko_rubi covered it well but just to add to it, a big advantage of running coilovers is that they have the potential to offer bigger travel than a standard coil and shock setup. Depending on how the mounts are designed, this "can" be done while still maintaining a low center of gravity. Coilovers can also be setup with 2 different spring rates of your liking and separated with a timing ring to give you greater control of how they'll feel for normal driving and how they'll respond under a heavy hit. Same is true of the valving as that too can be setup with different shim stacks. As mentioned, they are also adjustable or at least, to a degree and more preload can be set to compensate for a heavier load that you might be carrying. Of course, one of the biggest advantages of coilovers, my personal favorite and one that most people never really tap into, is how well they "can" perform while driving hard and fast across the desert. This goes back to the spring rates you can run and the valving you can set them up with. Also, the fact that they have big remote reservoirs will help keep them cooler and prevent the kind of cavitation that would normally occur in an old school hydro or even eventually occur in standard monotube shock.
With all that said, there are plenty of pitfalls to coilovers too, just as 13_gecko_rubi pointed out. First and foremost, UNLESS the mounts are designed well, you will most likely end up with a TALLER stance rather than a LCG and one that won't yield anymore vertical travel than a standard coil and shock setup would. Depending on what spring rates are used and how the valving is setup, you could also end up with a ride that sucks worse than the worst coil and spring setup. Also, coilovers can be noisy and they require maintenance which, unless you have a tall enough garage and can do it yourself, can be expensive and leave you with a Jeep sitting on very tall jack stands for as long as a month.
I could probably go on and on but the bottom line is, coilovers are far from needed for MOST people. Typically, I find that most people who get coilovers don't really have a clue about them and never use them for what they're made to really do. But of course, that's just me.
